<< programming

MATLAB

1. Basis

# Format

Semicolon is used to control whether to print the result of expression will be printed in the terminal (strange enough). Not print if semicolon is provided.

Use % to specifiy comments.

% This is one-line comment.
%{
This is multi-line comments.
Hello, I'm also the comments.
%}

# WorkSpace

MATLAB provides a visualized workspace to store the variables’ value. Use whos to show the variables in the workspace. Use save and load to save and load the workspace, so you can recover the variables’ value you solve before. (use extention .mat). A special variable ans is saved if a expression is not associated with an assignment, and will continue to exist in the workspace. The previous ans will be replaced if new unassigned result occurs.

a = 1;
b = 2;
a + b;       % The result of this expression is stored in `ans`
ans          % 3
a + b + ans  % 6, and it updates `ans`.
ans          % 6

You can use the direction keys to go through the history commands.

2. Matrix

Matrix is the first-class member in Matlab. All the variables are matrix. Single number is 1*1 matrix, and strings are 1*len(str) matrix (each element stores one char).

The function is designed to act on matrix, as so on the single variable as the 1*1 matrix.

Matrix Initialization:

% Manually
a = [1,2,3; 4,5,6; 7,8,9];

% Tool Functions
zeros(2,3); ones(2,3); rand(2,3);

% Colon Approach
a = 0: 5;  % [0,1,2,3,4,5]
a = 0: 0.2: 1;  % [0, 0.2, 0.4, 0.6, 0.8, 1.0]
% Notice that left/right endpoints are both included.

Matrix Subscripting:

a = [1,2,3; 4,5,6; 7,8,9];

% Matlab Start Index from 1.
a(2,2);  % Multidimensional indexing
a(5);        % Linear indexing


% Accessing non-exist index raise error, while the assignment will cause a matrix extension.
a(4,4) = 10

Some other usages of matrix including colon : is similiar with Python.

# Common Opeartion

a = rand(3,3);
c = sin(a);
b = a + 1;
adds = a + b;

Notice that the simple * opearator between matrix represents normal matrix multipication, use .* instead to the element-level multiplication. Besides multiplication, division and power also comply with this rule. This is different with numpy for Python, which use simple * as element-level multiplication to make the behaviour among operators fit.

# Matrix Special Operation

% Transposition
b = a';

# Concerntration

Using submatrix as element to profrom the concerntration. Notice the row or column must fit.

a = [1,2,3; 4,5,6; 7,8,9];
A = [a,a];
B = [a;a];

3. Graph

# 2-Dimensional

x = 0: pi/100: 2*pi;
y = sin(x);
plot(x,y);  % Use two 1-demensional matrix to generate 2d graph

Serval Configuration can be applied into the graph, which are actived synchronously.

xlabel('x');
ylabel('sin(x)');
title('Plot of the Sine Function');

Different plot command generate different graphes. Use hold on/off command to control if you want to plot in the same graph.

# 3-Dimensional

As the begin:step:end command in the 2D occasion, we use meshgrid command to construct a group.